Mathematically Proven Fact: Accelerate While Turning

Today I was chit chatting with my mentor about curvature and other differential-geometry-related shtuff, when she told me a most surprising fact. Unfortunately I can not explain it without relying on abstract mathematical concepts, because I myself can only understand it in those terms. It's really counterintuitive. Imagine you're driving on an exit ramp (or any any curved road for that matter). You want your acceleration vectors to point towards where you want your car to go, which in this case would be centripetally, towards the center of the circle in which you're driving. If you speed up, the acceleration vector gets longer, and pushes you more strongly to the center. If you decelerate, however, your acceleration vectors point backwards, away from where you want to go, so your car starts to skid. Of course it's good to slow down before making a turn. But once you start turning, you want to speed up. I'm talking nonsense? Well, that's what SHE said.

To understand this, do the following experiment:
Take a deep breath.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
Oh no! You're going to fast! You gently push the break.
Visualize it.
What do you feel happening?
I feel the tail of car swerving off the road.

Now let's try this again.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
As you start curving, you press the accelerator.
Visualize it.
What do you feel happening?
I feel the car griping the road.

These thought experiments are really worthless. It's possible that the reason I connect decelerating with losing control is because I usually slow down only if I'm going too fast to begin with. And I connect accelerating with control because I usually accelerate only if I started off at a slow enough speed. It's a shame she didn't tell me about this when I met with her last Wednesday. That way I could have experimented when I drove to Pittsburgh last Thrusday. All my passengers were screaming that I drive too fast. Wouldn't they love it if I told them that taking curves fast is safer? And then proceeded to demonstrate it experimentally?

But the bottom line is: you should definitely slow down before the curve. And if you are pulled over for speeding through a curve, explain to the cop that if you would have slowed down, you would have skidded off the road. Then pull out a pad and draw the acceleration vectors. The cop should excuse you, because math never lies.